1,460 research outputs found
Analytic solutions of the 1D finite coupling delta function Bose gas
An intensive study for both the weak coupling and strong coupling limits of
the ground state properties of this classic system is presented. Detailed
results for specific values of finite are given and from them results for
general are determined. We focus on the density matrix and concomitantly
its Fourier transform, the occupation numbers, along with the pair correlation
function and concomitantly its Fourier transform, the structure factor. These
are the signature quantities of the Bose gas. One specific result is that for
weak coupling a rational polynomial structure holds despite the transcendental
nature of the Bethe equations. All these new results are predicated on the
Bethe ansatz and are built upon the seminal works of the past.Comment: 23 pages, 0 figures, uses rotate.sty. A few lines added. Accepted by
Phys. Rev.
Solitons in the Calogero model for distinguishable particles
We consider a large two-family Calogero model in the Hamiltonian,
collective-field approach. The Bogomol'nyi limit appears and the corresponding
solutions are given by the static-soliton configurations. Solitons from
different families are localized at the same place. They behave like a paired
hole and lump on the top of the uniform vacuum condensates, depending on the
values of the coupling strengths. When the number of particles in the first
family is much larger than that of the second family, the hole solution goes to
the vortex profile already found in the one-family Calogero model.Comment: 14 pages, no figures, late
Growth models, random matrices and Painleve transcendents
The Hammersley process relates to the statistical properties of the maximum
length of all up/right paths connecting random points of a given density in the
unit square from (0,0) to (1,1). This process can also be interpreted in terms
of the height of the polynuclear growth model, or the length of the longest
increasing subsequence in a random permutation. The cumulative distribution of
the longest path length can be written in terms of an average over the unitary
group. Versions of the Hammersley process in which the points are constrained
to have certain symmetries of the square allow similar formulas. The derivation
of these formulas is reviewed. Generalizing the original model to have point
sources along two boundaries of the square, and appropriately scaling the
parameters gives a model in the KPZ universality class. Following works of Baik
and Rains, and Pr\"ahofer and Spohn, we review the calculation of the scaled
cumulative distribution, in which a particular Painlev\'e II transcendent plays
a prominent role.Comment: 27 pages, 5 figure
{\bf -Function Evaluation of Gap Probabilities in Orthogonal and Symplectic Matrix Ensembles}
It has recently been emphasized that all known exact evaluations of gap
probabilities for classical unitary matrix ensembles are in fact
-functions for certain Painlev\'e systems. We show that all exact
evaluations of gap probabilities for classical orthogonal matrix ensembles,
either known or derivable from the existing literature, are likewise
-functions for certain Painlev\'e systems. In the case of symplectic
matrix ensembles all exact evaluations, either known or derivable from the
existing literature, are identified as the mean of two -functions, both
of which correspond to Hamiltonians satisfying the same differential equation,
differing only in the boundary condition. Furthermore the product of these two
-functions gives the gap probability in the corresponding unitary
symmetry case, while one of those -functions is the gap probability in
the corresponding orthogonal symmetry case.Comment: AMS-Late
Human capital in the innovative conditions
The relevance of the questions dealing with the human capital formation and functioning peculiarities in the innovative development conditions is provided by the fact that highly developed post-industrial economy, manufacturing and service sector cannot do without highly educated and skilled workers, that makes dependable the efficiency and competitiveness at the company level and the whole national economy. The goal of the article lies in certain development within specific provisions in the economic science, which explain the human capital functioning and enhancing its role in the innovative development conditions. The leading approach to study this problem is the structure-functional analysis of the human role in advanced manufacturing and the innovation development when the human capacity to work transformed into capital, increasing the level of education and the formation on this new production relations basis in a modern knowledge economy. Results: the article puts forward the theoretical and methodological concepts dealing with the decisive role of human capital in modern knowledge economy, which is defined the qualitatively new productive forces composition, the science and education transformation in the main factors of efficiency, growth, intelligence, innovation production and management. The article can be useful in a problem-solving process one of the priority tasks in the Russian society – the human capital preservation and development and our country competitiveness in the innovative development conditions. © 2016 Forrester et al
Low-dose 2-Deoxy Glucose Stabilises Tolerogenic Dendritic Cells and Generates Potent in vivo Immunosuppressive Effects
Open Access via Springer Compact Agreement University of Aberdeen Development Trust Grant number RG14251, RG12663 Acknowledgements: We thank the University of Aberdeen Iain Fraser Flow Cytometry core facility, and the University of Aberdeen Histology and Microscopy core facility for processing of histology slides. The authors thank University of Aberdeen Medical Research Facility for technical assistance with in vivo experiments. We thank Dr. Tian Yu, Dr. Yi-Hsia Liu, Mrs Rosemary Fordyce, and Mrs Elizabeth Muckersie for technical assistance with in vivo and in vitro experiments. Funding: This work was supported by funds from the University of Aberdeen Development Trust Grants RG14251 and RG12663. Maria Christof was the recipient of a University of Aberdeen PhD Studentship. Samantha Le Sommer was funded by a Wellcome Trust ISSF Postdoctoral Fellowship.Peer reviewedPublisher PD
Off-diagonal correlations of the Calogero-Sutherland model
We study correlation functions of the Calogero-Sutherland model in the whole
range of the interaction parameter. Using the replica method we obtain
analytical expressions for the long-distance asymptotics of the one-body
density matrix in addition to the previously derived asymptotics of the
pair-distribution function [D.M. Gangardt and A. Kamenev, Nucl. Phys. B, 610,
578 (2001)]. The leading analytic and non-analytic terms in the short-distance
expansion of the one-body density matrix are discussed. Exact numerical results
for these correlation functions are obtained using Monte Carlo techniques for
all distances. The momentum distribution and static structure factor are
calculated. The potential and kinetic energies are obtained using the
Hellmann-Feynman theorem. Perfect agreement is found between the analytical
expressions and numerical data. These results allow for the description of
physical regimes of the Calogero-Sutherland model. The zero temperature phase
diagram is found to be of a crossover type and includes quasi-condensation,
quasi-crystallization and quasi-supersolid regimes.Comment: 17 pages, 7 figure
Spectrum of a spin chain with inverse square exchange
The spectrum of a one-dimensional chain of spins positioned at the
static equilibrium positions of the particles in a corresponding classical
Calogero system with an exchange interaction inversely proportional to the
square of their distance is studied. As in the translationally invariant
Haldane--Shastry model the spectrum is found to exhibit a very simple structure
containing highly degenerate ``super-multiplets''. The algebra underlying this
structure is identified and several sets of raising and lowering operators are
given explicitely. On the basis of this algebra and numerical studies we give
the complete spectrum and thermodynamics of the system.Comment: 9 pages, late
Universal correlations of trapped one-dimensional impenetrable bosons
We calculate the asymptotic behaviour of the one body density matrix of
one-dimensional impenetrable bosons in finite size geometries. Our approach is
based on a modification of the Replica Method from the theory of disordered
systems. We obtain explicit expressions for oscillating terms, similar to
fermionic Friedel oscillations. These terms are universal and originate from
the strong short-range correlations between bosons in one dimension.Comment: 18 pages, 3 figures. Published versio
Universal microscopic correlation functions for products of independent Ginibre matrices
We consider the product of n complex non-Hermitian, independent random
matrices, each of size NxN with independent identically distributed Gaussian
entries (Ginibre matrices). The joint probability distribution of the complex
eigenvalues of the product matrix is found to be given by a determinantal point
process as in the case of a single Ginibre matrix, but with a more complicated
weight given by a Meijer G-function depending on n. Using the method of
orthogonal polynomials we compute all eigenvalue density correlation functions
exactly for finite N and fixed n. They are given by the determinant of the
corresponding kernel which we construct explicitly. In the large-N limit at
fixed n we first determine the microscopic correlation functions in the bulk
and at the edge of the spectrum. After unfolding they are identical to that of
the Ginibre ensemble with n=1 and thus universal. In contrast the microscopic
correlations we find at the origin differ for each n>1 and generalise the known
Bessel-law in the complex plane for n=2 to a new hypergeometric kernel 0_F_n-1.Comment: 20 pages, v2 published version: typos corrected and references adde
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